Game cards



Aug. 31, 1926. 1,598,450

G. P. RITTER ET AL. l

GAME CARDS Filed sept. 29, 1924 2 shuts-Sheet 1 Il@ E @2W Lf-.WW 13 f".*........ o E z 26 6 i 7 2 1 @N3 [l 5 3 f/ g TZ l 4567samnuaeZ AAug. 31 1926. G. P. RITTER'v ET Al.

GAME' CARDS Filed sept. 29, 1924 2 slums-sheet` 2 m mrmfwmw N N N n M M m Nll; W v @55 M N, im E A M o lill gnou/1410@ Wim GILBERT P. RITTER, OF W'ASHINGTON, AND EDVJEN L. BRADFORD, OE TAKOMA PARK, DSTRICT OF CGLUMBA.

GAME

Appli' cation led September This invention relates to a set of game jards designed to enable speed and accuracy in the fundamental processes of arithmetic to be acquired by the playing of games in which the cards are used. The cards are designed not only for drill but also to. teach the facts in the multiplication and division tables, when knowledge of these more diflicult number-relations has not been acquired in advance. This is accomplished by the ease with which the beginner can in'- stantly determine from the cards themselves the correct answer for any multiplication or for any fundamental problem of division, while the repeated occurrence throughout the play of all the various mutliplications from two times two up to twelve times `twelve, together with the related division facts, ultimately fastens these number-relations, making them intimately familiarized material held ever ready for instant and automatic use.

The character of the cards is such `that they easily lend themselves to the playing of games which are simple variations of the `familiar card games universally played and enjoyed. The games played with the cards therefore achieve the three-fold advantage of possessing` the interest inherent in the games upon which they are based, of being easily learned and of being desirably instructive.

The invention essentially consists in providing a set of cards each of which bears an index number together' with a number forming a part of the answer to an arithmetical problem based on its index number and that of another card, the answer forming numbers on one card being complemental to those on other cards of the set. l Y

Another feature of the invention consists in providing a set of cards wherein each card bears an index number together with a number forming a part of the answer to an arithmetical problem based on its index number and that of another card, the answer forming numbers on one card being complemental to those on othercards of the set, and each card bearing indicia constituting means for determining the appropriate compleinental vnumbr-irs xto Ibe read together CARDS.

2e, 1924i. serial No. 740,546.

to obtain the answer to the problem based on the index numbers of any two cards.

Other features of the invention will hereinafter appear and be particularly pointed out in the claims.

In the drawings illustrating a set of cards" constructed in accordance with the invention for the purpose of teaching the facts in the multiplication and divisi-on tables Figure l is a view displaying the faces of a group of cards forming part of a set of cards employing the invention, the cards of the group respectively bea-ring the index numbers 2, 3, 4l, 5, 6 and 7.

l Figure 2 is a similar view of the remaining cards of the illustrated set, said cards respectively bearing the index numbers 8, 9, l0, 1l and 12. l

Figure 3 is a face view of two of the cards overlapped in proper relation for disclosing the product resulting from multiplying their index numbers.

The pack may advantageously consist of fifty-five cards, comprising live sets of eleven cards each. Such a pack, since it has approximately the same number of cards as contained in a pack of common playing cards, lends itself particularly well to the playing of games which are simple variations of the proper games played with ordinary playing cards.

In the particular embodiment of the invention illustrated in the drawings the index numbers a of the cards of each set are consecutive from 2 to l2 and may be placed `on the cards at diagonally opposite corners thereof. The paclr thus contains live cards of each denomination, 2, 3, 1l, 5, etc., cards bearing the index numbers O and l being omitted because the product result-ing from multiplying O by any number is O, and the product resulting from multiplying any number by l is the number itself.

Preferably arranged along the top and bottom e lges of each card are two rows yof guide numbers Zi, which may advantageously be printed in red and have adjoining corresponding dots. The guide numbers of each row read consecutively from 2 to l2 in the same direction, preferably from left to right. Disposed along an edge or lnargiVVA ot each card, preferably the lett hand edge, a column oi bordering numbers c, which may be printed in black and each ot which is preferably bounded on thr e sides by red box lines d separating them trom .each each other and 'from the numbers e scattered over the body o'f the card, these latter seats tered numbers preferably being in blacl; in correspondence with the bordering numbers c. The `scattered numbers e are likewise bounded on three sides by red box lines` f. The bordering numbers c on each card are complemental to the scattered numbers e on all the other cards, so that when any two cards are overlapped (see Fig. 3) on the line indicated by the appropriate guide num sers b on the under ard, there is formed at the lett hand edge of the upper card a completely closed bo:" made up `from ad jacent box lines, d and j on the two cards, l/Vithin this` box are. embraced numbers appearing on both cards, one ot said numbers being a bordering number c and the other a number e appearing on the body ot the under card. "When read together the two numbers in the closed box show the correct product due to multiplying the index number of one card by that ot the other. Conversely, the index numbers on the two cards are the factors of the product appearing in the completed box.

For the sake of symmetry it is pret'erred that the column ot bordering figures c on each card shall consist ot ten numbers. It is, however, not necessary to have ten bordering numbers c on each card. @n those bearing the odd index numbers 3, 7, 9 and ll all the numbers from 0 to 9, inclusive, are required; on the card having the index number o bordering numbers O and 5 alone are necessary; on those having the index number 10 the bordering number 0 need only be used; and on cards bearing even index numbers 2, t, 6, 8 and 12 only even bordering numbers 2, A, 6 and S together with O are required. The reason for this will be apparent upon noting that the bordering numbersl c at the lett hand edge ofthe card occupy the units place in the answer showingl the result ot multiplying the index numbers of any two cards, and upon considering that the numbers 3, 7, 9 and ll when mul-- tiplied by various numbers running consecutively trom 2 to 12 produce products in which all the numbers from 0 to 9', inclusive, appear in the units place in the answer; Similarly when 5 is multiplied by any number the resulting answer ends either in 0 or in 5; when lO is multiplied. by any number the resultinganswerends in O; and when 2, e, 6', Sor 12; is multiplied by any number the resulting answer ends either in O, 2, il, 6' or 8.

The ca rdbearing thelindex. number l0 preferably has among its bordering numbers c two zeros. As either of these zeros may be read with complemental numbers e on the other cards of the set to disclose the product resulting from multiplying any number by 10, the employment o'lf a plurality oi zeros on the l() card permits a disposition oit the numbers c scattered on the bodies ot the other cards which is less crowded than would be possible it a single bordering number O were employed on the l() card.

The numbers e scattered over the` body of each card are in horizontal alinement with the respective numbers c at the lett hand edge ot the card and are spaced horizontally so that they are out ot vertical alinement, each number c being so disposed that it stands immediately to the lett ot the line passing through two of the dots associated with the respective pairs 01": guide numbers 2 2, 3 3, d-r, etc., along the top and bottom edges oi the Card. Thus it will be seen that when any two cards are overlapped so that the lett hand edge of the upper one passes through the two dots corresponding tothe index number of the upper card, the appropriate number c which is to be read in conjunction with a bordering number o of the uppermost card will appear immediately adjacent the lett hand edge of the said upper card.

The ar langement oi bordering numbers c and scattered numbers e appearing on the set ot cards illustrated in the drawings is a desirable one in that it results in spacing the numbers c advantageously; but it will be understood that the bordering numbers c may be arranged in a dii'l'erent order which, ot course, will result in corresponding changes in the positions ot the scattered numbers c. In fixing the positions of the scattered numbers ou a set ot cards, the desired order o't the bordering numbers c upon any card may be established, after which this card may be suc essively overlapped in appropriate position on the other cards ot the set and `the positions ot the various scat.- tered nun'ibers e on those cards be suitably adjusted so as to read with the established bordering numbers. The position ot the bordering and scattered numbers o and c, respectively, ot the other cards oit the set may thereafter be obtained by similarly overlapping the various cards of the set with each other and marking thereon the required bordering and scattered numbers in their proper positions.Y

As the number-relations involved in multiplication are more difficult than those of division, the set of cards chosen tor the purpose of illustrating the invention is based upon the fundamental problems of multiplication and division.

When inthe course of any game it is necessary to check`the result ofmultiplying'any Jill lli

two of the index numbers of the cards, either card is placed on the other in such position that (see F ig. 3) their top and bottom edges match while the lett hand margin of the upper card passes through the dots associated with the guide numbers on the lower card corresponding to the index number or denomination oithe upper card. lWhen thus positioned certain ofthe box lines CZ and f match on the two cards, and a single completely closed box or rectangle is formed at the left hand edge of the top card within which the correct answer appears. For example, if the result of multiplying 4; by 7 is to be checked, the t card may be positioned on top ot' the 7 card, or vice versa. If the t card is placed on top, its lett hand edge is alined with the dots corresponding to the guide numbers 4---4 at the upper and lower edges of the 7 card; it the 7 card is placed on top its left hand edge is alined with the guide numbers 7 7 on the 4; card. In either case, certain lines d and 7 on the two cards match at the left hand edge of the top card tocomplete a rectangular frame or box enclosing the correct answer 28, the number 2 being onone card and the number i being on the other.

Since the index numbers or denominations of any two properly overlapped cards are the iactors of the number appearing in the closed rectangle formed by t-he box lines CZ and f, the index number of either card accordingly gives the quotient resulting from dividing the number in the closed rectangular box by the index number o1 the other card. It thus possible instantly to check the correctness of any players statement as to the factors corresponding to the number appearing in the closed box .of any two properly overlapped cards, and also to check the accuracy of his answer to the problem of dividing the number in the closed box by the index number oit either of the overlapped cards.

l? or the purpose ot' illustrating the character of games which may be played with the cards, rules for two games are here set forth, one et said games being much like Casino and involving problems of multiplication, and the other being an adaptation of the well known game of Authors and involving problems ot division.

First game.

The pack: F ull pack of cards.

Number of players: Two, three or four. (Partners, two against two.)

Dealing: Deal tour cards to each player and four to table, two at a time in rotation, beginning with the player at the dealers lett. The cards to the table are dealt face up, just before the. dealer serves himself. The remainder ot' the pack is left face down on the table, and after the first hand has been played, four more cards are dealt to each player as before; but none to the table. This continues until all oit the cards have been dealt and played. Deal passes to the lett.

Object of the game.

To sriore points by taking in certain cards and card combinations with counting value as follows:

Cards (greatest number of cards taken in) 3 points.

Duros (greatest number of cards taken in ot' denominations 7, 8 and 9) 2 points.

Little Sixes "r'our cards oi denomination 6) l point.

Big Sixes (tive cards ot denomination G) 2 points.

Little Twelves7 (four cards of denomination l2) 2 points.

Big 'lwelves7 (five cards of denomination i points.

Sweep (taking in all cards on table) l point. (By agreement sweeps may not be counted.)

The play: Each player, beginning with the player immediately to the left of the dealer, .may make any of the following plays:

(l) Take in a combination; i. e., if he holds a card in his hand in sequence with one on the table or in sequence with two or more of the same denomination), he may play his card and take in both (or all such cards), provided he correctly announces at the time of playing his card the product resulting trom multiplying the two cards together. It the card played from his hand is in sequence with two cards on the table oi different denominations, one higher and the other lower than the card played, he may play his card and take in all three provided he correctly announces the products obtained by multiplying his card with each of the other two. Along with these three he may take in all others on the table of corresponding denominations. F or example, one or more nines may be taken by either an 8 or a l0; if taken by an 8 the player should announce 72 (i. e. 8X9) on playing the card from his hand.r and if taken by a l() should say (i. e. 10 9). 0r one or more eights and one or more tens on the table may be taken by a 9 from the players hand upon announcing 72 (i. e., 9X8) and 90 (i. e., 9 10). But any combination taken in by playing from the hand a card in sequence with one or more cards on the table must leave at least one card remaining on the table; that is to say, no sweep is permitted to be made by playing a card which is in sequence with vall cards on the table.

It another player questions the correctness of any announced multiplication he says check and thereupon the player who has announced the multiplication must place the player must leave both cards on the table.

*iii

a combination olf two or more cards by addinga card from his hand to one or more cards on the table, provided he holds in his hand another card whose denon'iination is in sequence with the niunber representing the sum ot such cards. Un his next turn to play he may take in thev build by playing a card ot denomination in sequence therewith, provided no other player has taken it *ith a card in He may build sequence with its sum, or has built higher on it, and provided also that the correct multiplication roduct is announced. rhus, it a 3 on the board and the player holds a 5 and a 9, he can build his on the thus making 8, and can take it with the Q on his nent` turn upon announcing the correct multiplication TQ (i. e., 9X8); or similarly, he could the build with a T upon announcing' ad t 7X8).

He may call a combination; thus, it he holds a 7, along; with either a or an 8 and there on the board another 17, or any coinbination olt cards whose sum equals 'I ,5i-k2; or @rl-3; or l-l-Q-i-Q), he may play his l on all such cards on the board, callingthe resulting` assemblage seven-sl; and he (or any other player) may take them on his nent turn by A Iaying either a or an t5, provided he correctly announces the result olt the correspending` multiplication (for instance, the player announces d2 itt the sevens are taken with a 6, and 5G they are taken with an 8). lt the announced innltiplication is checked and proves to be incorrect the card with which the player attempted to take the called combination forfeited and is placed `tace upward vith any other cards which may be on the board. The 'torteited card is never made a part ot the called' combination. 'Vhile a build can be built. higher, a call cannot, because the call contains more than one combination.

(1l) A sweep is a card which takes in every card on the table at once, Sweeps are noted by Ylacing' one card ot the combination in which the sweep is made.

(5) lt a player cannot make any combination, he plays single card tace up to the board.

Alter pack is exhausted, last player taking; in combination also takes all cards remainii on the board, but taking the remaining car ls in this way does not constitute a sweep.

Rules: A player cannot raise his own build, unlesshe has the cards to take in both the first build and the raised one.

A player may make a second builder a call,v or may take in a con'ibination, or cap-y ture anothers build or call before taking in his lirst build or call, otherwise he must take in hisl iirst build or call at his next turn to play.

Cards once taken in cannot be examined, except the last con'ibinat-ion won; nor points nor cards counted until all the cards have been played. A mistake in announcing; a multiplication cannotbe corrected atter it has been questioned; nor can it be challenged at'ter another combination has been taken in.

A card pl yed out of turn must be withdrawn and held until the players proper turn to play, when it must be played to the table. Player in error cannot combine it during that hand, or win any combination ot cards with it. liny cards taken in with it by odending player must be restored to the table.

Builds may be' raised with cards 'from the hand only; never with cards Jfrom the table. Builder or caller must announce the denomination of the build or call; otherwise other player may separate the cards and use any of them.

A player taking in a card not belongingto his coml'iination or build must restore it and all other cards in the combination or build to the table, and his own card is laid out separately trom the others. lt the combination was his own, the cards comprising1 it must be separated; it an opponents, the combination must be left intact. A player taking in combination with a wrong card, taking' in a wrong combination or card not belonging to him must be challenged and the error proved before the next combination is taken in. lt a` player makes a build or a call without having` in his hand the proper card to take it, he must upon discovery ot the error break such combination, leaving the cards in separated relation on the table. Opponents cards played after the error may be taken back and different cards playe'l it opponents elect. It' the build improperly made by one player has been taken by another player, there is no penalty nor any remedy.

Game: First player' scoring` 3l points wins. The points score out in the following` order: Cards, duros, big twelvcs, big sixes, little twelves, little sixes, and sweeps.

Second game.

The pack: Full pack of cards.

Number of players: From two to tire.

Dealing: Deal nine cards to each player, one at a time, in rotation to the left, live tace clown and Jfour tace up, the first round being; dealttace down and succeeding rounds alternately Jface up and face down. The remainder of the pack is placed in the center ot the table tace down. Deal passes to the left. Each player arranges his four exposed cards in a row before him face up, picking up the live other cards.

Object 07 the game.

The object ot each player is to show before him on the table eight cards arranged in four pairs, each pair consisting of two cards of the same denomination.

The play: rlhe dealer begins by holding up any two cards from his hand; he states the number resulting from multiplying their index numbers together, and demands of the next player to his lett an answer to the problem or' dividing the stated number by the index number oit one ot' the cards. rlhe denomination of the other card is the correct answer to the problem, and therefore the players response can be checked immediately. For instance, the dealer, holding up a 7 and a 12 so that their backs are toward the player on his left, says: 84 by 7, meaning by this short form of expression 8adivided by 7 equals what? rlhe dividend 84 in this division problem is the result obtained by multiplying the denominations of the two cards together (that is, 7 12:84) g while the quotient or correct answer is the denomination of the l2 card. Il, on the other hand, the question asked on these two cards is 84 by l2 (that is, 84-3-12: i) then the correct answer is the denomination oi the 7 card.

It a. player whose turn it is to act as questioner does not surely know the number resulting from multiplying the denominations ot the two cards he desires to hold up, it is only necessary for him to hold the cards in proper overlapped relation, when he may instantly read the required number in the completely closed red box7 appearing` at the lett hand edge of the upper card.

(l) it the answer to the question is incorrect, the answering player orieits for that turn the right to use a card from his hand to form a pair with one of his exposed cards; and he may not draw a card fronti the hand of any player or from the pack, or from the discard beside the pack, nor may he discard any card from his hand or from his exposed cards; but he shall immediately hold up two cards trom his hand and ask the next player on his lett a division qu-estion based upon them.

(r2) It the answer given is incorrect, the questioner so indicates by stating the correct answer. Thus it the questioner 4says G3 by Y (that is, (iS-I-Tz?) and the player incorrectly answers 8, the questioner shall say 9 Should the answering player doubt that he has answered incorrectly, he may demand that the questioner check the two cards upon which the question was asked. The questioner then must show both cards and shall, it called upon to do so, arrange them in proper overlapped relation to permit the dividend used in the question to be cchecked.

(3) It th-e question asked is not correctly based on the two cards which the questioner holds up, the answering player shall so declare by saying` error. The questioner sha-ll then show and check the cards on which the question is asked. If the question proves not to be based on the cards, the answering player shall remove one card from any pair exposed before the questioner and shall place it in the discard; the questioner then draws a card from the pack and takes it into his hand. For instance, if the vquestioner', holding up a 9 and a 7, Says 56 by 9 (instead of 63 by 9), the answeringplayer shall say error, thus compelling the questioner to suffer the penalty of losing a card from any exposed pair he may have.

(at) It' the answering player mistakenly claims error in a correct question, itshall be deemed the same as if an incorrect answer had been given.

(5) lf the answer to the question is correct the answering player may: (a) either draw one c rd from the hand of any other player; or draw a card from the top of the pack; or (c)- draw a card from the discard. Il a card is drawn from aplayers hand he replaces it immediately, drawing al card from the top ot' the pack, or from the discarded cards beside the pack before the player who has drawn from him dise cards, thus being prevented Jfrom iminediately taking back the card just drawn from him.

(6) After the player who has correctly answered has Vseen the card he has drawn, he may use it or any other card from his hand to form a pair with anycard of the saine denomination exposed before him and not already paired; or he may substitute tor any one of his exposed cards the card he has drawn or any other that he holds. Only one pair can be formed at a time, and only one exposed card can be substituted for at time. It a pair is formed, a card may not be substituted for an exposed card, and vice versa. ln any case, the player must discard one card face down on the table beside the pack after having drawn a card. li' he wishes to form an exposed pair, or wishes to replace one of his exposed cards with another, the player must not discard until after he has made the desired play, because by discarding he signifies that he either cannot or does not wishto torni a pair or replace an exposed card, and thereupon his right to do so is forfeited. After discarding, the play-er shall hold up two cards Yfrom his hand and ask the next player on his left a division question based upon them.

(7) When the last card is drawn tromthe lli) paci: the discard is shuffled and formed into a new pack, which is placed down on thek table and drawn from as beiiore.

The 'play 'continues in this manner until one ot the players has eight cards exposed on the table. cor'ibined in pairs.

ocoiing. ne nist person to expose ioui pz irs wins th gaine and scores one point Ytor each exposed card vremaining impaired on the table. kept with chips ra nl Iiithc score i (of which each player 'has an equal number to begin with) the winner collects from the other' players according to the number ot unpaired tarde each has before him.

lirhat is claimed is l. A set of cards7 each card bearing an imlex numbertogether with a number torming a part ot the answer to an arithmetical problem based on its index. number and that of another card, the answer forming numbers on one card being complemental to those on other cards of the set.

A set ot cards, each card bearing an index number togetherwith a number forming a part of the answer to an arithmetical problem based on its index number and that ot' another card, the answer 'forming numbers on one card being complemental to those on other cards of the set, and each card bearing indicia ior enabling any two cards to be overlappingly positioned so as to determine appropriate complemental numbers to be read together to obtain the answer to the problem based on the index numbers ot the two cards.

S. A set of cards, each card bearing an index number together with a number tornr ing a part oithe answer to an arithmetical problem based on its index-number and that of another card, the answer r'forming numbers on one card being complemental to those on other cards of the set, and each card bearing indicia constituting means for determining the appropriate complemental numbers to be read together to obtain the answer to the problem based on the index numbers ot any two cards.

il. A set of cards, each card bearing an index number together with a plurality of numbers each respectively forming a complemental part of the product obtained by multiplying` the index number of the card by the index number of another card ot the set.

5. A set of cards, each card bearing an index number together with a plurality of numbers each respectively forming a complemental part ot the product obtained by multiplying the index number ot the card by itself or by the index number ot another card ot the set.

6. A 'set of cards, each cardlbearing 'an "index number togetherV with a plurality of:

numbers scattered over the body of the card and including a Zero adjacent va margin ot the card, thesaidzero on each card being adapted to be read in conjunction with one oli the numbers on the body of another card to give the product resulting from multiplying the index numbers ot the two cards.

i'. A set ot cards, each card bearing an index number together with a plurality o' numbers arranged in two groups, the nurnbers of one group being arranged along a margin ol they card and being adapted to be read :in conju'nction with numbers appearing on the other cards to give th product resulting trom multiplying the index numbers 0i." any two cards, said marginally arranged numbers on cards bearing odd index numbers other than the index number including all numbers Ytrom l to 0, inclusive, and also a zero, and the marginally arranged numbers on the card bearing the index number 5 including a zero and 8. A set ot cards, each card bearing an index number together with a plurality ot numbersarranged intwo-groups, the numbersoi one group being arranged along a margin otthe'card and being adapted to be read in conjunction with numbers appearing on the other cards to give the product resulting from multiplying the index numbers of any two cards, said marginally arranged numbers on c'ards bearing even index numbers other than the index number l() including the even numbers two, tour, ix and eight and also a zero.

9. A set of cards, each card bearing an index number together with a plurality ot' numbers arranged in two-groups7 the numbers of one group being arranged along a margin ot the card and being adapted to be read in conjunction with numbers appearing on the other cards to give the product resulting from multiplying the index numbers of any t'vo'cads, and the said marginal numbers ot the card bearing the index number l() comprising a plurality or zeros.

l0. A set of cards, each card bearing a plurality ot numbers adapted when the card is overlapped in a predetermined relation with each of the other cards to be read in conjunction with numbers on the other cards to complete the answers to a system ol? arithmetical problems, each olf said cards being'provided with indicia tor establishing the respectively proper overlapping positions ot the other cards.

l1. A set oi cards, each card bearing an index number together with a plurality o'i numbers corresponding to the several index numbers borne by the cards ot' the set, said plurality of numbers providing means for indicating the yproper relative position in which any'two cards are to be placed to disclose the answer to an arithmetical problem basedon the index numbers oi the said two 'cards, and each `card also carrying a plurality of numbers in 'addition to those hereliu based on the index totore mentioned, said last named numbers on each card being complemental to those on other cards of the set and forming with the latter the answers to arithmetical problems numbers ot the cards.

12. A set of cards, each card bearing au index number together with a plurality ot numbers arranged in two groups, the numbers of one group being scattered over the body of the card and those of the other group being arranged along a margin ot the card and being adapted to be read in conjunction with said scattered numbers appearing' on the other cards to give the answer to an arithmetical problem based on the index numbers of any two cards, the said scattered numbers and those along the margin of the card having indicia associated therewith constituting` means for determining the appropriate numbers on any two cards which are to be read together to give the answer to an arithmetical problem based on the index numbers thereot.

13. A set ot cards, each card bearing an index number, a plurality of oppositely disposed rows of numbers, the numbers in each row being arranged in the same order and corresponding to 'the several index numbers borne by the cards of the set, and a plurality ot numbers arranged in two groups, the numbers of one of said groups being scat-- tered over the body of the card and those ot' the other group being arranged in alignment along a margin oi the card, the numbers in the said groups on each card being complemental to those in the said groups on other cards and forming with the latter the answers to arithmetical problems based on the index numbers of the cards.

141-. A set of cards, each card bearing an index number, a plurality of rows oit num-A bers arranged along opposite margins ot' the card, the numbers in each row being an ranged in the same order and corresponding to the several index numbers borne by the cards ot the set, a row of numbers bordering` another margin of the card, and a plurality oi1 numbers scattered over the body ot the card, the said scattered numbers and those in said last named row on each card beim 2 complemental to numbers on other caras and forming therewith the answers to arithmetical problems based on the index numbers oi the cards.

15. A set o'f cards, each card bearing an ir dex number and a plurality ot numbers arranged in two groups, the numbers in each group being complemental to numbers ap- `ciated pearing on other cards and forming therewith the answers to arithmetical problems based on the index numbers ot' the cards, and the numbers in each group on each card being respectively associated with indicia which upon properly overlapping any two cards are adapted to mate with corresponding complemental indicia assowith the numbers in the groups on other cards so as to indicate the numbers lon the two cards which are to be read together to give the answer to the arithmetical problem based on the index numbers of the two cards.

16. A set oit cards, each card bearing an index character, a plurality of characters belonging` to the same system and arranged in two groups, and a plurality of characters corresponding to the several index characters borne by the cards ot the set and arranged to provide means for determining the proper overlapping relation 'of any two cards, the characters in either of said groups on each card being adapted to be read in conjunction with characters appearing in other groups on other cards ot the set to complete the answer to probleins involving the index characters ot' any two cards.

17. A plurality of cards each bearing an index number, each and every two ot said cards bearing numbers adapted to be read together to give the product resulting from multiplying the index numbers ot the two cards.

18. A set of cards, each card bearing an index number together with a plurality ot numbers arranged in two groups, the numbers of one group being' disposed along a margin ci4l the card and those of the other group being scattered over the body ot' the card, the numbers in each group being adapted to be read in conjunction with numbers appearing on the other cards to give the product resulting from multiplying the index numbers ot any two cards.

1.9. A set o1"l cards, each card bearing an index number and a plurality of characters in addition thereto, said characters on each card being' complemental to those on yother cards and being adapted in conjunction with the latter to complete the answers to a set ot' arithmetical problems based. on the index numbers of the cards.

ln testimony whereof we aitix our signatures.

GlLBERT P. RTTER. EDWTIN L. BRADFGRD. 

